Stratifications, Equisingularity and Triangulation
| Autor: | David Trotman |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Trotman, David |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Triangulation (topology)
Pure mathematics 010102 general mathematics [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG] [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] 16. Peace & justice Lipschitz continuity 01 natural sciences Stratification (mathematics) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] 0103 physical sciences [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV] Isotopy 010307 mathematical physics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 0101 mathematics [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG] [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT] Stratum Mathematics |
| Zdroj: | Introduction to Lipschitz Geometry of Singularities Introduction to Lipschitz Geometry of Singularities, pp.87-110, 2020 Introduction to Lipschitz Geometry of Singularities ISBN: 9783030618063 |
| Popis: | International audience; This text is based on 3 lectures given in Cuernavaca in June 2018 about stratifications of real and complex analytic varieties and subanalytic and definable sets. The first lecture contained an introduction to Whitney stratifications, Kuo-Verdier stratifications and Mostowski's Lipschitz stratifications. The second lecture concerned equisingularity along strata of a regular stratification for the different regularity conditions: Whitney, Kuo-Verdier, and Lipschitz, including thus the Thom-Mather first isotopy theorem and its variants. (Equisingularity means continuity along each stratum of the local geometry at the points of the closures of the adjacent strata.) A short discussion follows of equisingularity for complex analytic sets including Zariski's problem about topological invariance of the multiplicity of complex hypersurfaces and its bilipschitz counterparts. In the real subanalytic (or definable) case we mention that equimultiplicity along a stratum translates as continuity of the density at points on the stratum, and quote the relevant results of Comte and Valette generalising Hironaka's 1969 theorem that complex analytic Whitney stratifications are equimultiple along strata. The third lecture provided further evidence of the tameness of Whitney stratified sets and of Thom maps, by describing triangulation theorems in the different categories, and including definable and Lipschitz versions. While on the subject of Thom maps we indicate examples of their use in complex equisingularity theory and in the definition of Bekka's (c)-regularity. Some very new results are described as well as old ones. |
| Databáze: | OpenAIRE |
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